Phase retrieval is the numerical procedure of recovering a complex-valued signal from knowledge about its amplitude and some additional information. Here, an indirect registration procedure, based on the large deformation diffeomorphic metric mapping (LDDMM) formalism, is investigated as a phase retrieval method for coherent diffractive imaging. The method attempts to find a deformation which transforms an initial, template image to match an unknown target image by comparing the diffraction pattern to the data. The exterior calculus framework is used to treat different types of deformations in a unified and coordinate-free way. The algorithm performance with respect to measurement noise, image topology, and particular action are explored through numerical examples.

翻译：相位恢复是一种从信号幅度及相关信息中恢复复值信号的数值方法。本文研究了一种基于大变形微分同胚度量映射（LDDMM）形式的间接配准方法，并将其作为相干衍射成像的相位恢复技术。该方法通过将衍射图样与数据进行比较，寻找一种形变，将初始模板图像变换以匹配未知目标图像。研究采用外微分框架，以统一且无坐标依赖的方式处理不同类型的形变。通过数值实例，探讨了该算法在测量噪声、图像拓扑及特定作用下的性能表现。